How do I animate the position of my character's hair randomly?
Adding a force field works with the correct settings.

I use a turbulence field with a large strength and small size. I added a #frame driver to each location and rotation channel, to make it change transformations frame by frame.



In the hair dynamics, make sure to set mass, stiffness and damping to low values. Since my low stiffness value would cause the particles to completely loose their shape, I increased the goal weight.